High-Frequency Variable Load Inverter and Related Techniques

ABSTRACT

Inverter systems, circuits and associated control techniques for providing efficient delivery of high-frequency (HF) power and radio-frequency (RF) power into variable load impedances while maintaining resistive/inductive loading of the constituent inverters for zero voltage switching (ZVS) are described. The inverter architecture and associated control techniques for providing efficient delivery of HF into variable load impedances includes a first inverter having an output coupled to an input of an immittance converter. An output of the immittance converter is coupled to a second inverter. The second inverter maybe either serially or parallel coupled between the output of the immittance converter and a load.

CROSS REFERENCE TO RELATED APPLICATION

This application claims the benefit under 35 U.S.C. §119(e) of U.S. Provisional Application No. 62/355,414 filed Jun. 28, 2016, which application is incorporated herein by reference in its entirety.

BACKGROUND

As is known in the art, many applications, ranging from industrial plasma generation to wireless power transfer, require inverters (or power amplifiers) that can deliver power at high frequency (HF), e.g. 3-30 MHz or Very High Frequency (30-300 MHz) or above to a load circuit (or more simply, a “load”). Such applications often utilize signals having frequencies which fall with the industrial, scientific and medical (ISM) band of frequencies (e.g., 6.78 MHz, 13.56 MHz, 27.12 MHz). The loads coupled to an output of the inverter to receive HF power therefrom may often exhibit load impedances that vary over a wide range. Such impedance variations include variations in both inductive and capacitive impedance characteristics as well as resistive variations.

As is also known, addressing such applications with circuits and systems which operate at a relatively high efficiency is challenging owing to the constraints imposed by the combination of HF operation and varying impedances of loads. Inverter designs at HF generally utilize fundamental-frequency inductive loading of the inverter transistor(s) to achieve zero-voltage switching (ZVS) transitions necessary to achieve high efficiency operation. Also for efficiency reasons, it is desirable to provide only a minimum amount of inductive loading necessary to support ZVS along with the current needed to support the load. Providing HF power to a load having a highly-variable load impedance (particularly into a load impedance having variations in inductive and capacitive impedance characteristics in addition to resistive variations) makes it difficult to maintain desired inductive transistor loading without requiring a large inductive circulating current, which itself can induce substantial loss. Thus, variations in load impedances (i.e. loading variations) can directly constrain an achievable operating range and efficiency of an inverter system. Furthermore, these constraints become increasingly severe with increasing frequency and power ratings.

One approach to address load impedance variations in some applications is to augment an inverter designed for a single load impedance (e.g., 50 Ohms) with a tunable matching network (TMN) that dynamically matches the variable load impedance to the fixed value desired for the inverter. Such TMNs realize the adaptive tuning using variable passive components, such as motor-driven mechanically-variable capacitors, switched capacitor banks, or high-power varactors. This approach is very effective since it allows the inverter to operate at its designed operating point for all loads within the tuning range of the TMN. The TMNs themselves, however, are generally expensive, bulky, slow and inefficient. Thus, efficient generation and delivery of power into variable load impedances is difficult, resulting in HF inverter (or power amplifier) systems that are bulky, expensive and inefficient.

SUMMARY

Described herein are inverter system and circuit architectures and associated control techniques which allow direct delivery of high frequency (HF) power to load circuits (or more simply “loads”) having impedances which vary over a wide range.

In accordance with one aspect of the concepts, systems, circuits and techniques described herein, a system comprises a pair of inverters coupled and controlled such that each inverter always has presented thereto a load impedance having a resistive/inductive characteristic with the inductive loading component limited to that necessary for supplying any reactive component of a load current while at the same time realizing zero-voltage switching (ZVS) of both inverters.

Such an approach enables power delivery systems to directly provide power into highly variable load impedances with a relatively high efficiency. The described inverter architecture and associated control approach enable efficient delivery of radio-frequency (RF) power into loads having widely varying impedances (i.e. widely variable loads) while maintaining efficient zero-voltage switching (ZVS) operation.

In accordance with a further aspect of the concepts, systems, circuits and techniques described herein, an inverter architecture and associated control approach for providing efficient delivery of HF into varying load impedances includes a first inverter having an output adapted to be directly connected to the load wherein the first inverter is coupled such that its output is coupled in series or in parallel with the load, an immittance converter, and a second inverter having an output coupled to the load through the immittance converter and wherein the immittance converter is configured to be coupled in parallel or series with the load.

With this particular arrangement, a power delivery system having an architecture which results in a region of load admittances over which the system can efficiently operate within inverter constraints as a function of output power is provided. The inverter system further includes a controller coupled to provide control signals to the first and second inverters such that a capacitive susceptive portion of a load current is substantially provided by the second inverter via the immittance converter, and an inductive susceptive portion of a load current is substantially provided by the first inverter. In embodiments, the systems, circuits and techniques provide efficient delivery of HF into variable load impedances while maintaining resistive/inductive loading of the constituent inverters for ZVS soft switching.

In accordance with a further aspect of the concepts, systems, circuits and techniques described herein, a control method includes setting in-phase and quadrature phase components of first and second inverters to achieve a desired output power and inverter loading characteristics. By controlling in-phase (I) and quadrature (Q) components of a voltage common as provided to first and second inverters the I/Q representation carries the same information as the magnitudes and phases of the inverter voltages and defining the I/Q relationships such that the quadrature component for each inverter leads its in-phase component by 90° and the in-phase component of the second inverter leads that of the first inverter by 90°. The in-phase component of the first inverter (V_(AI)) may be arbitrarily defined to be the desired output voltage phase reference such that the voltage of the first inverter is defined by its in-phase component and has zero quadrature component (V_(AQ)=0). The in-phase component of the second inverter (V_(BI)) may be defined as leading the in-phase component of the first inverter by 90°. Thus, in terms of phasors. V_(A)=V_(AI) and V_(B)=−V_(BQ)+jV_(BI).

With this particular arrangement, a control technique which achieves output control goals (i.e. delivering a specified output power while preserving desired inverter loading characteristics) for loads within an achievable range is provided.

The architecture and techniques described herein result in a relatively compact, cost effective circuit which enables efficient generation of HF power for applications in which load admittance varies over a wide range.

In accordance with the concepts, systems, circuits and techniques described herein, an inverter system capable of dynamically adjusting to impedance variations of a load coupled to an output thereof, the inverter system comprising a pair of inverters and an immittance converter.

With this particular arrangement, an HF inverter which can directly operate efficiently across a wide range of load impedances is provided. That is, the inverter may be directly coupled to a load (i.e. without a TMN coupled between the inverter and the load) to dynamically adjust to variations in a load impedance thereby resulting in a system having a relatively high efficiency compared with efficiencies achieved using prior art approaches.

In embodiments, the pair of inverters may be provided as a pair of HF zero voltage switching (ZVS) inverters. By interconnecting the ZVS inverters with an immittance converter and a load network, the amplitudes and relative phases of the inverters may be controlled to: modulate output power; and realize inductive/resistive loading of both inverters for ZVS soft switching under both capacitive and inductive loading.

In embodiments, an HF inverter provided in accordance with the architecture described herein may directly drive and control power into a wide range of load impedances at HF and VHF frequencies (e.g. in the 3-300 MHz frequency range). Furthermore, an HF inverter provided in accordance with the architecture described herein may maintain resistive/inductive loading of the inverters for ZVS soft switching while directly driving and controlling power into a wide range of load impedances.

In embodiments, high-frequency inverters for some applications operate with variable resistive/inductive loading. In such applications, ZVS Class D or DE inverters are suitable and the inverter system may include an optional inductive preload circuit to enable ZVS with pure resistive loading.

In embodiments, high-frequency inverters for some application operate with variable resistive/inductive loading. Variable-load Class E inverters are also suitable since variable-load class E inverters work well under both inductive and variable resistive loading.

In accordance with a further aspect of the concepts, systems, circuits and techniques described herein, a method for providing efficient delivery of high frequency (HF) power into a load having a variable load impedance includes (a) controlling a first inverter to achieve a desired radio frequency (RF) power level at an RF output thereof; and (b) controlling a second inverter such that the second inverter drives substantially any capacitive component of the first inverter loading to substantially zero, and a quadrature-phase component of a voltage command provided to the second inverter becomes zero when the load is inductive such that the second inverter delivers a real component of the output power having an amplitude within its voltage rating while concurrently maintaining an in-phase current sourced by the first inverter to be substantially zero or positive such that the first and second inverters have presented thereto a load impedance having a resistive/inductive characteristic.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing features may be more fully understood from the following description of the drawings in which:

FIG. 1A is a block diagram of a variable load inverter;

FIG. 1B is a block diagram of an alternate embodiment of a variable load inverter;

FIG. 2 is a phasor diagram illustrating voltage and current relationships in the network of FIG. 1A for a load having inductive susceptance;

FIG. 3 is a phasor diagram illustrating voltage and current relationships in the network of FIG. 1B for a load having capacitive susceptance;

FIG. 4 is a plot of constraints vs. load conductance which illustrates voltage and current constraints determining allowable inverter operating range as a function of load conductance;

FIG. 5 is a plot of susceptance vs. conductance which illustrates the region of the load admittance plane that can be driven by the systems of FIGS. 1A, 1B for resistive/inductive loading of each inverter an assuming an output power of level P≦P_(r,i);

FIG. 6 is a plot of imaginary vs. real components of load admittance;

FIG. 7 is a plot of imaginary vs. real components of load admittance;

FIG. 8 is a Smith chart which illustrates achievable operating ranges for the system of FIG. 1A for different normalized output power levels (illustrating reflectance and admittance);

FIGS. 9A-9F are a series of phasor representations of system voltages and currents for different load admittances with V_(M)=1, I_(M)=1, Z₀=1 and P=0.5 P_(r,i)=025 using the control approach specified in Table I;

FIG. 10 is a schematic diagram of an example circuit implementation of a system having a high frequency variable load inverter architecture based on zero-voltage switching (ZVS) class D inverters with inductive preload networks and a lumped “T” implementation of an immittance converter; and

FIGS. 11A and 11B are plots of voltage vs. time for an inverter system which may be the same as or similar to the system of FIG. 10.

DETAILED DESCRIPTION

In general overview, described is a new architecture for HF variable-load inverters which Incorporates two ZVS soft-switched HF inverters and an immittance converter. The amplitudes and phases of inverters can be controlled so as to enable delivery of RF power into a wide range of varying load impedances (both capacitive and inductive loads) while maintaining resistive/inductive loading of the inverters for ZVS soft switching.

The concepts, systems, circuits and techniques described herein find use in a wide variety of applications requiring power in the HF (3-30 MHz) or VHF (30 MHz-300 MHz) frequency ranges. In general, concepts, systems, circuits and techniques described herein may find use in any application in which RF energy must be delivered to a load having a wide range of load impedances (i.e. the impedance characteristic of the load dynamically varies (i.e. changes while the system is operating). Such applications include, but are not limited to plasma generation, induction heating, wireless power, magnetic resonance imaging (MRI) applications. Some applications may be narrow-band (e.g., ISM band 6.78 MHz, 13.56 MHz, 27.12 MHz).

Referring now to FIG. 1A, an inverter system 10 for delivering power at high frequency (HF) e.g. frequencies in the range of 3 MHz-30 MHz comprises a pair of inverters 12 a, 12 b, (e.g. switched mode inverters) with a first one of the inverters 12 a directly coupled to a load 14 and a second one of the inverters 12 b coupled to the load 14 via an immittance converter 16. Immittance converter 16 is here illustrated as a T network provided from lumped components. Those of ordinary skill in the art will appreciate, of course, that immittance converter 16 may also be provided from a distributed circuit such as a quarter-wave transmission line section or from a combination of lumped and distributed circuit components.

For reasons which will become apparent from the description hereinbelow, the inverter system also comprises a controller coupled to provide control signals to the first and second inverters, to dynamically vary at least one of bias input voltages and/or ac output voltages and relative switching phases of the first and second inverters 12 a, 12 b so as to control the delivery of HF power to the load 14.

Thus, as illustrated in FIG. 1A, the two HF ZVS inverters 12 a, 12 b, are interconnected with immittance converter 16 and load network 14 and the amplitudes and relative phases of the inverters may be controlled to modulate output power and realize inductive/resistive loading of both inverters for ZVS soft switching under both capacitive and inductive loading.

Referring briefly to FIG. 1B, in which like elements of FIG. 1A are provided having like reference designations, a variant of the system described in FIG. 1A is shown. It should be appreciated that the alternative embodiment of FIG. 1B can be used to provide the same advantages as the embodiment of FIG. 1A in terms of inverter loading. It should also be appreciated that in the embodiment of FIG. 1B, the location of inverter 12 a and the load may be exchanged to make the inverter ground referenced.

One difference between the embodiments of FIGS. 1A and 1B is that the architecture of the system illustrated in FIG. 1A is more suitable for supplying loads requiring large transient currents at limited voltage, while systems having the architecture illustrated in FIG. 1B are advantageous for supplying loads requiring large transient voltages at limited current. In either case, however, one inverter (i.e. inverter 12 a in the illustrative embodiments) is directly connected to the load (with an output in series or parallel with the load), while the other inverter (i.e. inverter 12 b) is coupled to the load via an immittance converter (with one port of the immittance converter in parallel or series with the load).

Referring again to FIG. 1A, for modeling purposes and to explain the operation of the proposed architecture, the inverters are treated as ideal ac voltage sources having controllable amplitude and phase. In practice, one can utilize any type of inverter suitable for HF operation under resistive/inductive loading, and amplitude control of the individual inverters can be realized through any suitable means (e.g., supply voltage modulation, phase-shift or outphasing control, pulse-width modulation, etc.).

The immittance converter 16 serves to losslessly transform the voltage (current) delivered by inverter 12 b at the first port of the immittance converter into an appropriately-scaled and phase-shifted current (voltage) at the second port of the immittance converter and vice versa, according to the following rule:

$\begin{matrix} {\begin{bmatrix} V_{A} \\ I_{Z} \end{bmatrix} = {\begin{bmatrix} 0 & {{- j} \cdot Z_{0}} \\ \frac{- j}{Z_{0}} & 0 \end{bmatrix} \cdot \begin{bmatrix} V_{B} \\ I_{B} \end{bmatrix}}} & (1) \end{matrix}$

An immittance converter is thus a two-port lossless, reciprocal network that swaps between voltages and currents at its ports (with a 90° delay). For example, a quarter-wave transmission line is an immittance converter. Also, many lumped circuit implementations of an immittance converter are available. An immittance converter “inverts” impedances—e.g. an Impedance Z_(L) on one port is presented as (looks like) an impedance value of Z₀ ²/Z_(L) at the other port.

Thus, immittance converter 16 has a characteristic such that the immittance converter swaps voltages and currents between its ports, consequently transforming between capacitive and inductive impedances. Such a characteristic is important to the operation of a power delivery system having the proposed architectures described herein. In practice, the immittance converter can be realized with a variety of passive lumped networks and at sufficiently high frequencies can be realized with a quarter-wave transmission line. Immittance converter 16 may, for example, be the same as or similar to the type described in (M. Borage, K. V. Nagesh, M. S. Bhatia and S. Tiwari, “Resonant Immittance Converter Topologies,” IEEE Transactions on Industrial Electronics, Vol. 58, No. 3, pp. 971-978, March 2011).

The amplitudes and relative phase of the two inverters 12 a, 12 b are used to control both the total output power and the effective loading admittance presented at the ports of each of the two inverters. It should be appreciated that as used herein the phrase “effective loading admittance,” refers to the complex ratio of current to voltage at an inverter output port with both inverters active. In particular, the relative phases and amplitudes of inverters 12 a, 12 b are controlled in a manner such that each inverter 12 a, 12 b are presented a resistive/inductive effective load regardless of the nature of the actual system load, facilitating zero-voltage switching (ZVS) of the inverters.

With reference to prior art systems, it is noted that a classical Doherty rf power amplifier utilizes an immittance converter to combine power from two sources into a single output and has an architecture which provides in-phase combining of power from linear power amplifiers into a specified resistive load (yielding resistive load modulation of the amplifiers),

The present architecture, on the other hand, utilizes both amplitude and phase shift control among switched-mode inverters to achieve both power control and desirable resistive/inductive loading of the constituent inverters across a wide range of load impedances.

For simplicity of explanation, inverter controlled is explained in terms of the conductive and susceptive components of the load admittance.

Which inverter supplies the susceptive component of the load current depends upon whether the susceptive component is inductive or capacitive. In the case where the load is inductive, the susceptive portion of the load current I_(LB) is provided by inverter 12 a, while the conductive portion of the load current I_(LG) is split between inverters 12 a, 12 b.

In contrast, when the load is capacitive, the susceptive portion of the load current I_(LB) is provided by inverter 12 b (after processing through the immittance converter), while the conductive portion of the load current I_(LG) is split between inverters 12 a, 12 b. In each case, the relative phases of inverters 12 a, 12 b can also be set to ensure a degree of inductive loading for each inverter to provide soft switching we treat each of these cases in turn.

To further explain the broad concepts sought to be protected herein, and with reference to FIGS. 2 and 3, consider an inductive/resistive load as illustrated by the phasor relationship of FIG. 2 and only use of inverter 12 a. In this case, inverter 12 a is inductively loaded (for ZVS). Next, with reference to FIG. 3, consider a capacitive/resistive load and only use of inverter 12 b. Through action of the immittance converter 16, the capacitive/resistive load appears as an inductive/resistive load to Inverter 12 b. Thus, inverter 12 b is also is inductively loaded (for ZVS).

Consider next the interaction of the two inverters (neglecting load). With appropriate phasing between components of V_(A), V_(B), both inverters see an inductive loading component owing to the action of the immittance converter. This provides reactive currents facilitating ZVS switching of both inverters. Thus, operated together, inverter 12 a supplies reactive current for inductive loads and inverter 12 b supplies reactive current for capacitive loads while one or both inverters may deliver real power. Thus, the two inverters 12 a, 12 b can cover a wide load admittance range with inductive loading (for ZVS) of both inverters.

Referring now to FIG. 2, as noted above, a phasor relationship for the example where a load (e.g. load 14 in FIG. 1A) is conductive/inductive is shown. The load voltage may be directly set by the voltage of inverter 12 a, with amplitude V_(A) (as identified by reference numeral 20) set to a level sufficient to drive the desired average load power. It should be noted that a zero-phase reference for voltage V_(A) is arbitrarily assumed. The phase of inverter 12 b voltage V_(B) is set to an angle (θ_(B)+90°) ahead of the phase of inverter 12 a voltage V_(A) owing to the action of the immittance converter 16, the current I_(B) lags V_(B) by θ_(B), providing a degree of inductive loading for inverter 12 b. Angle θ_(A) is selected to be as small as possible commensurate with providing both inverters 12 a, 12 b, with desirable operating waveforms (e.g. waveforms which provide sufficient inductive currents to each inverter for ZVS switching.)

In the case where the inverters 12 a, 12 b are designed such that they can achieve ZVS with a purely resistive load, θ_(B) can be set to zero. Owing to the action of the immittance converter 16, current I_(Z) leads V_(A) by θ_(B). The amplitude V_(B) is selected such that the sum of the real components of I_(Z) and I_(A) are sufficient to support the necessary load conductance current I_(LG). The imaginary component of I_(A) is negative, representing the difference between the susceptive component of the load current I_(LB) and the imaginary component of current I_(Z). I_(A) thus lags V_(A), providing inverter 12 a with a degree of inductive loading.

The detailed achievable operating range is described below, however, FIG. 2 illustrates that for any conductive or conductive/inductive load admittance, each of the two inverters 12 a, 12 b can be provided with desirable loading conditions (e.g., for ZVS soft switching).

Referring now to FIG. 3, as noted above, a phasor diagram illustrates an example in which a load is conductive/capacitive. As described above in conjunction with FIG. 2, the load voltage and output power are again set by the voltage of inverter 12 a and the phase of inverter 12 b voltage V_(B) is likewise set to an angle (θ_(B)+90°) ahead of V_(A). In this case, however, the phase θ_(B) is selected in conjunction with the amplitude of V_(B) such that the imaginary component of related current I_(Z) provides the susceptive portion of the load current I_(LB) along with any necessary additional current to enable soft switching of the two inverters.

Owing to this additional (imaginary axis) current, the phase of current I_(A) lags V_(A) by a small amount (θ_(A)), thereby providing an inductive loading component to inverter 12 a. For an inverter which is preloaded for ZVS soft switching under resistive load, θ_(A) can be zero, while without preloading, θ_(A) can be just sufficiently large in conjunction with the amplitude of I_(A) that the resulting susceptive component of I_(A) suffices to realize a voltage transition for zero-voltage switching.

Likewise, phase θ_(B) provides a sufficient inductive loading component for inverter 12 b. If the inverters 12 a, 12 b, are designed to achieve desired operation into a resistive load, phase θ_(B) can be selected such that θ_(A) is zero, making current I_(A) in phase with V_(A)).

As can be seen from FIGS. 2 and 3, by utilizing the appropriate controls, loads with either capacitive or inductive susceptive components can be supplied with the proposed system while maintaining resistive/inductive loading of each inverter (e.g., for ZVS soft switching). A more detailed control strategy by which the above goals can be realized is described below.

Of interest in the proposed architecture is the achievable load admittance range that can be driven as a function of inverter VA rating and specified output power. In the example provided herein, focus is placed on the symmetric case in which the two inverters 12 a, 12 b are substantially identical, each with an ac output current amplitude rating Wand ac output voltage amplitude rating V_(M) and with characteristic impedance of the immittance converter of Z₀=V_(M)/I_(M)=1/Y₀. Each inverter 12 a, 12 b thus has an ideal rated output power of P_(r,i)=½·−V_(M)·I_(M), though this output power is only achievable into a single effective load impedance. Consequently, the system 10 is typically operated at a power level which is well below P_(r,i).

Described below is an analytical treatment of the range of load admittances that can be driven within inverter operating limits as a function of the desired output power (normalized to the power rating of a single inverter P_(r,i)). The analysis starts by establishing the load conductance range over which a single inverter can drive a desired average power P assuming zero susceptance. Equations 2 and 3 show the required load voltage amplitude [V_(OUT), equal to V_(A) in FIG. 1A] and conductive load current amplitude [I_(L)] necessary to drive power P as a function of conductance G.

$\begin{matrix} {{V_{OUT}} = \frac{\sqrt{2\; P}}{\sqrt{G}}} & (2) \\ {{I_{G}} = {\sqrt{2\; P} \cdot \sqrt{G}}} & (3) \end{matrix}$

Referring now to FIG. 4, the above relationships are illustrated along with constraints on inverter voltage and current, with curve 34 corresponding to the current constraint and curve 36 corresponding to the voltage constraints. G_(MIN) denotes the minimum load conductance for which power P can be delivered within the specified inverter voltage rating V_(M). For lower conductances, power P cannot be delivered without exceeding the inverter voltage limit. Similarly, G_(MAX1) is the maximum load conductance for which a single inverter can deliver sufficient current to drive power P within inverter current rating I_(M). Given that two inverters are available to deliver power, there is an extended load conductance range over which a specified power P could be delivered by the system. G_(MAX2) shows the maximum conductance for which both inverters operating together (e.g. inverters 12 a, 12 b) could deliver the current required to provide power P (at zero susceptance). These load conductance values can be found to be

$\begin{matrix} {G_{MIN} = {{\frac{2\; P}{V_{M}^{2}}\mspace{31mu} G_{{MAX}\; 1}} = {{\frac{I_{M}^{2}}{2\; P}\mspace{31mu} G_{{MAX}\; 2}} = {4\frac{I_{M}^{2}}{2\; P}}}}} & (4) \end{matrix}$

The real part of the load admittance range that can be supported is defined by G_(MIN), G_(MAX1), G_(MAX2). To find the complete admittance range that is supportable, first consider the typical case of power levels P≦P_(r,i) for which G_(MIN)≦G_(MAX1)<G_(MAX2). For operation between G_(MIN) and G_(MAX1), the system is not constrained by voltage, and the real (conductive portion) of load current can be completely supported by one of the two inverters. This leaves the second inverter to support the susceptive portion of load current up to its maximum rated current I_(M). Based on the current delivery constraint of the second inverter, the necessary current can be provided for susceptances having magnitudes up to a value B_(MAX):

$\begin{matrix} {{B_{MAX}} = {\frac{I_{M}}{\sqrt{2\; P}} \cdot \sqrt{G}}} & (5) \end{matrix}$

Operating between G_(MAX) and G_(MAX2), current contributions from both inverters are needed to support the conductive component of the load current. This leaves a portion of current from one of the inverters remaining to support susceptive load components, which may be shown to yield a maximum susceptance amplitude for this range of conductances:

$\begin{matrix} {{B_{MAX}} = \sqrt{\frac{G}{2\; P} \cdot \left( {{2\; I_{M}\sqrt{2\; {PG}}} - {2\; {PG}}} \right)}} & (6) \end{matrix}$

Referring now to FIG. 5, a plot of susceptance vs. conductance which illustrates a region of a load admittance plane that can be driven by the systems having an architecture in accordance with the concepts described herein for resistive/inductive loading of each inverter (assuming an output power level of P≦P_(r,i)) is shown (i.e. FIG. 5 illustrates a load admittance range at power P within an inverter ac output voltage and having current ratings V_(M) and I_(M)).

As can be seen from FIG. 5 when load conductance G reaches G_(MAX2), all available current is being delivered to the load conductance, and the achievable susceptance is zero as indicated by reference numeral 50.

To further delineate the achievable operating range, the largest susceptance magnitude that can be driven while providing power P to the load conductance is found. This susceptance magnitude is denoted as B_(BP), and the load conductance (between G_(MAX1) and G_(MAX2)) at which this peak susceptive drive capability is reached as G_(BP). Differentiating Equation (6) with respect to G and setting this derivative to zero yields:

$\begin{matrix} {B_{BP} = {{\frac{3\sqrt{3\; I_{M}^{2}}}{8\; P}\mspace{31mu} G_{BP}} = \frac{9\; I_{M}^{2}}{8\; P}}} & (7) \end{matrix}$

This boundary result is likewise indicated in FIG. 5.

It will be appreciated that the range of load admittances that can be driven is a function of an average power P, with lower power corresponding to a wider region of admittances.

Referring now to FIG. 6, a plot of imaginary vs. real components of load admittance illustrates a region of the load admittance plane that can be driven by a system provided in accordance with the concepts described herein for different normalized output power levels. The achievable operating range of load admittances that can be driven (normalized to a characteristic admittance Y₀=1), is illustrated for specified output powers of 0.5 (curve 52), 1 (curve 54) and 1.5 (curve 56) times P_(r,i) (i.e. FIG. 6 illustrates an achievable range of load admittances at different power levels −1.5P_(r,i), 1.0P_(r,i), 0.5P_(r,i)).

From curves 52, 54, 56, it can be seen that the load admittance range that can be driven increases rapidly with reductions in commanded power (or, equivalently, with increases in the volt-ampere ratings of the inverters relative to a desired output power). Thus, from FIG. 6 it can be thus be appreciated that to enable operation over a wide range of load admittances, one may oversize the VA ratings of the inverters.

The boundaries of the operating region are directly linked to inverter constraints. For example, the vertical boundary of a minimum load conductance directly expresses the voltage output limit of inverter 12 a and current output limit of inverter 12 b, while the boundaries to the right reflect complementary constraints.

At power levels below P_(r,i) G_(MIN)<G_(MAX1), the region is delineated just as illustrated in FIG. 5, with the area encompassed diminishing as P increases at P=P_(r,i), G_(MIN)=G_(MAX1), while for higher values of P, G_(MIN)>G_(MAX1), such that the inverter voltage limit increasingly constrains the achievable admittance region. The area of allowable admittances continues to decrease with increasing power collapsing to a single point Y=2Y₀ at P=2P_(r,i).

Referring now to FIG. 7, a plot of imaginary vs. real components of load admittance illustrates regions of a load impedance plane that can be driven by a system provided in accordance with the concepts described herein for different normalized output power levels. It should be noted that the same constraints on allowable load range as a function of power described above can be expressed as regions of the load impedance plane. Results are shown normalized to a characteristic impedance Z₀=1. It should be appreciated that the curves of FIG. 7 reflect the same operating boundaries as FIG. 6.

Referring now to FIG. 8, Smith chart results are shown normalized to a characteristic admittance of Y₀=1. This plot reflects the same operating boundaries as FIGS. 6 and 7.

It can be observed that the admittance regions encompassed in FIGS. 5, 6 and 8 are symmetric about zero susceptance, and the impedance regions in FIG. 7 are symmetric about zero reactance. It should, of course, be appreciated that the operating ranges can be made nonsymmetric by inclusion of “offset” reactance(s) in shunt and/or series with the load.

Also, it should be noted that the operating boundaries indicated in FIGS. 5-8 assume the use of inverters which operate well under all of pure resistive, pure inductive, and combination resistive/inductive loading. Thus, to meet these boundaries, the inverters must be able to efficiently supply a purely resistive load. Inverters requiring external inductive loading can be accommodated by adjusting the relative inverter phases such that each inverter sees a sufficient inductive load through action of the immittance converter (as illustrated in FIGS. 2 and 3), while incurring a degree of reduction in the operating boundaries. In the description below, it is assumed that the inverters are designed to operate with any combination of resistive and inductive loading within their voltage and current ratings.

There are many high-frequency inverter designs that can operate well within the constraints of resistive/inductive loading described above. One option is a ZVS class D or class DE inverter having either a matching network or inductive pre-load network such that it can operate with soft switching into a variable resistive/inductive load. Another option is an appropriately-designed single-switch inverter (e.g., class E, class φ₂, etc.). While “classical’ Class-E inverter designs impose significant constraints on loading to maintain ZVS, some single-switch inverters are suitable for variable-load operation, In particular, the variable-load class E design and other single-switch inverter designs introduced in (L. Roslaniec, A. S. Jurkov, A. Al Bastami and D. J. Perreault “Design of Single-Switch Inverters for Variable Resistance/Load Modulation Operation,” IEEE Transactions on Power Electronics, Vol. 30, No. 6, pp. 3200-3214, June 2015.) can operate with low loss across a wide range of resistive, resistive/inductive and inductive loads. While some systems only explicitly treat design for variable load resistance, the resulting inverter designs can maintain ZVS and low loss for resistive/inductive and pure inductive loads as well, so long as the active switch has an antiparallel diode or equivalently provides reverse conduction. Modulation of the individual inverter output amplitudes (as necessary for the proposed architecture) may be relatively easily realized by modulating the inverter supply voltages (e.g., using dc-dc converters to vary the inverter dc supplies, also known as “drain modulation”), though other means are also possible.

It should be noted that the operating points on the boundaries of FIGS. 5-8 reflect the most extreme loads that can be driven at the specified power levels by inverters operating within maximum peak ac voltage and current rating V_(M) and I_(M). As such, there is typically only one set of control commands (inverter amplitudes and phases) that can support these operating points. By contrast, there are many combinations of amplitudes and phases that can support many interior points (as one could divide power between the two inverters in various ways for these interior points). This, in turn, means that there are multiple ways the system can be controlled to achieve the desired output. Many of these control means share the above-described characteristic of which inverter takes on the supply of the susceptive portion of the load current (after compensating any offset components in the susceptive range) depending upon whether this susceptive portion is inductive or capacitive. Described below is one possible control strategy.

One possible control strategy (explained herein in terms of in-phase and quadrature components of inverter voltages) may be as follows. An in-phase component of V_(A) (denoted as V_(AI)) sets an output power level, provides any inductive portion of load current and provides any conductive portion of load current not supplied by V_(B). A quadrature component of V_(A) (denoted as V_(AQ)) is set to a reference value (e.g. zero). An in-phase component of V_(B) (denoted as V_(BI)) is set to provide an amount of a conductive portion of a load current within inverter voltage limit V_(BI)≦(V_(M) ²−V_(BQ) ²)^(1/2). In preferred embodiments, the in-phase component of V_(BI) is set to provide as much of the conductive portion of the load current as possible within inverter voltage limit. A quadrature component of V_(B) (denoted as V_(BQ)) provides capacitive portions of the load current and sets additional reactive current for ZVS switching. Such control strategy results in an inverter system capable of dynamically adjusting to varying impedances of a load coupled to an output thereof.

As noted above, the example control strategy described herein is based upon in-phase and quadrature components of the voltage common as provided to inverters 12 a, 12 b. This I/Q representation carries the same information as the magnitudes and phases of the inverter voltages. The I/Q relationships can be defined such that the quadrature component for each inverter leads its in-phase component by 90°, and the in-phase component of inverter 12 b leads that of inverter 12 a by 90°. The in-phase component of inverter 12 a (V_(AI)) may be arbitrarily defined to be the desired output voltage phase reference such that the voltage of inverter 12 a is defined by its in-phase component and has zero quadrature component (V_(AQ)=0). The in-phase component of inverter 12 b (V_(BI)) may be defined as leading the in-phase component of inverter A by 90°. Thus, in terms of phasors. V_(A)=V_(AI) and V_(B)=−V_(BQ)+jV_(BI). To achieve the desired control goals, the in-phase and quadrature components of the two inverters may be selected as shown in Table I (i.e. Table I shows a control method based upon setting in-phase and quadrature components of the inverter voltages to achieve the desired output power and inverter loading characteristics).

TABLE I V_(AI) Set amplitude (within 0 ≦ V_(AI) ≦ V_(M)) to achieve desired reference output power P_(o,ref) (V_(AI) is thus used to set output power). V_(AQ) Set to zero (by definition of the desired phase of V_(A)). V_(BQ) Set within 0 ≦ V_(BQ) ≦ V_(M) to drive I_(AQ) to zero (V_(BQ) is thus used to drive any capacitive component of inverter A loading to zero, and becomes zero when t load is inductive). V_(BI) Set within 0 ≦ V_(BI) ≦ (V_(M) ² − V_(BQ) ²)^(1/2) to drive I_(AI) towards 0⁺ limited by the requirement on V_(BQ) above and by the allowed total operating voltage of invert (V_(BI) is thus set such that inverter B will deliver as much of the real component the output power as possible within the voltage rating of inverter B and while maintaining the current sourced by inverter A to be zero or positive).

This control technique (supported by appropriate measurements and feedback compensators) can provide a desired output and inverter loading characteristics across the operating range.

FIGS. 9A-9F are a series of phasor representations of system voltages and currents for different load admittances with V_(M)=1, I_(M)=1, Z₀=1 and P=0.5 P_(r,i)=0.25 using the control approach specified in Table I. The load admittances correspond to some of the boundary operating points specified in FIG. 5;

Thus, FIGS. 9A-9F show the resulting inverter voltages and current phasors using the above-described control technique for six of the boundary operating points indicated in FIG. 5 (six load admittances at P=0.5·P_(r,i) with normalized inverter ratings V_(M)=1, I_(M)=1 and Z₀=1). The relationships between inverter 12 a voltage (V_(A)) and inverter 12 b current (I_(B)), and inverter 12 b voltage (V_(A)) and immittance converter output current (I_(Z)) are apparent.

FIGS. 9A-9F illustrate that inverters 12 a, 12 b both maintain resistive/inductive loading for all operating points. Moreover, it can be seen that any capacitive component of load current is provided by inverter 12 b through the immittance converter 16, while any inductive component of load current is provided directly by inverter 12 a.

Referring now to FIG. 10, an example circuit implementation of a system 70 having a high frequency variable load inverter architecture provided from zero-voltage switching (ZVS) class D inverters 72, 74 with inductive preload networks 76, 78 and a lumped “T” implementation of an immittance converter 79. Component values for operating at a switching frequency of 13.56 MHz are shown in Table II.

TABLE II V_(INA) 0-160 V_(DC) V_(INB) C_(SA1), C_(SA2), C_(SB1), C_(SB2) 1 μF L_(SSA) L_(SSB) 100 nh Q_(A1), Q_(A2), Q_(B1), Q_(B2) R_(ON) = 50 mΩ C_(OSS) = 40 pf L_(TA), L_(TB), L_(PFA), L_(PFB) 470 nH C_(TA), C_(TB), C_(PFA), C_(PFB) 294 pF L_(IC1), L_(IC2) 117 nH C_(IC) 117 nF

The example circuit of FIG. 10 thus represents a simulated 13.56 MHz inverter system having component values as shown in Table II (i.e. Table II shows component values for the example inverter system of FIG. 10).

The ZVS class D inverters (operated with 11 ns switching deadtime) utilize the inductive preload networks to provide ZVS soft switching under resistive or resistive/inductive loading. The immittance converter has a characteristic impedance of 10Ω and is realized as a T network. Notional values for V_(M) and I_(M) are 100 V and 10 A, respectively, though these are only approximate in practice. The inverter devices are modeled as having 50 mΩ on-state resistance and 400 pF output capacitance, commensurate with available devices. The inverters are each provided with series and parallel filter networks 77, 78 tuned at the switching frequency for harmonic reduction. The dc input voltages and relative switching phases of the two inverters are dynamically varied to control the system in accordance with the concepts and techniques described herein. Such control may be implemented through control system 75 and bias system 76 (e.g. a drain voltage bias system).

FIGS. 11A, 11B are LTSPICE simulations showing the behavior of an inverter system which may be the same as or similar to the example system of FIG. 10 having the values show in Table II. This system operations at a frequency 13.56 MHz with a system characteristic admittance of Y₀=0.1.

Referring now to FIGS. 11A and 11B, shown are example simulation results for a system which may be the same as or similar to the system of FIG. 10. Curves 81, 82 correspond to the unfiltered outputs of the ZVS soft-switched inverters 12 a 12 b and curves 84 and 86 are their respective currents (providing resistive and/or inductive loading of the inverters). Curve 88 corresponds to the output (load) voltage.

FIG. 11A illustrates operation with a resistive/capacitive load comprising a 5Ω resistor in parallel with a 2.34 nF capacitor (representing an admittance of approximately 0.2+0.2j). This operating point is achieved with dc input voltages V_(IN,A)=80 V and V_(IN,B)=160 V, with the fundamental output voltage component of inverter B leading that of inverter A by approximately 180°.

FIG. 11B illustrates operation for a resistive/inductive load comprising a 5Ω resistor in parallel with a 58.7 nH inductor (representing an admittance of approximately 0.2-0.2j). This operating point also utilizes dc input voltages V_(IN,A)=80 V and V_(IN,B)=160 V, but with the fundamental output voltage component of inverter 12 b (FIG. 1A) leading that of inverter 12 a by approximately 90°. These two operating points correspond approximately to those of the middle column in FIG. 9 (with values appropriately renormalized for V_(M), I_(M) and Z₀).

It can be seen that zero-voltage switching of each inverter is maintained for both the resistive/capacitive and resistive/inductive load cases. Moreover, the output waveforms match well with the underlying theory. For the resistive/capacitive case, the ac output voltage has a peak value of 48.6 V and the system delivers 234 W, while in the resistive/inductive case the peak ac output voltage is 48.8 V, and the system delivers 238 W. These simulation results illustrate the ability of the architecture and control/operating techniques described herein to operate with a wide range of load impedances including both capacitive and inductive loads and show how such a system might work with practical inverter designs. 

What is claimed is:
 1. An inverter system having an output with the output configured to be coupled a load, the inverter system comprising: a first inverter having an output adapted to be directly connected to the load wherein the first inverter is coupled such that its output is coupled in series or in parallel with the load. an immittance converter having first and second ports; and a second inverter having an output coupled to the load through said immittance converter and wherein said immittance converter is configured such one of said first and second immittance converter ports is coupled in parallel or series with the load; and a controller coupled to provide control signals to said first and second inverters such that a capacitive susceptive portion of a load current is substantially provided by said second inverter via said immittance converter, and an inductive susceptive portion of load current is substantially provided by said first inverter.
 2. The inverter system of claim 1 wherein the first inverter is coupled such that its output is in parallel with the load.
 3. The inverter system of claim 1 wherein said first inverter is coupled such that its output is in series with the load.
 4. The inverter system of claim 1 wherein said controller is coupled to said first and second inverters and configured to controlling at least one of the inverter output voltages by controlling an inverter bias voltage.
 5. The inverter system of claim 1 further wherein said controller is coupled to provide control signals to said first and second inverters and is configured to dynamically vary each of the inverter output voltages and relative output phases of the first and second inverters to control the system.
 6. The inverter system of claim 5 wherein said controller controls the first and second inverters such that each inverter always has presented thereto a load impedance having a resistive/inductive characteristic with the inductive loading component limited to that necessary for supplying any reactive component of a load current while at the same time realizing zero-voltage switching (ZVS) of both inverters.
 7. The inverter system of claim 5 wherein any capacitive susceptive portion of load current is substantially provided by said second inverter via said immittance converter, and any inductive susceptive portion of load current is substantially provided by said first inverter.
 8. The inverter system of claim 1 further comprising first and second preload networks coupled to respective ones of said first and second inverters and configured to provide zero voltage switching (ZVS) under resistive or resistive/inductive loading.
 9. The inverter system of claim 1 wherein the immittance converter is realized as a T network.
 10. In an inverter system having a first [Inverter A] directly coupled to a load with an output in parallel or in series with the load and a second inverter [Inverter B] coupled to the load through an immittance converter with one port of the immittance converter in parallel or series with the load, a method of operating the inverter system comprising: (a) setting an in-phase component of a voltage command (V_(AI)) to the first inverter [Inverter A] to achieve a desired radio frequency (RF) power level at an RF output of the second inverter [Inverter B]; (b) setting a quadrature-phase component of a voltage command (V_(AQ)) to the first inverter [Inverter A] to a first reference value; (c) setting a quadrature-phase component of a voltage command (V_(BQ)) to the second inverter [Inverter B] such that the second inverter [Inverter B] drives a capacitive component of the first inverter [Inverter A] loading to substantially zero, and wherein the quadrature-phase component of a voltage command (V_(BQ)) to the second inverter becomes zero when the load is inductive; and (d) setting an in-phase component of a voltage command (V_(BI)) to the second inverter (Inverter B) such that the second inverter [Inverter B] delivers a real component of an output power which is within the voltage rating of second inverter [Inverter B] while maintaining an in-phase current sourced by first inverter [Inverter A] to be zero or positive.
 11. The method of claim 10 wherein setting an in-phase component of a voltage command (V_(AI)) to the first inverter comprises: setting a voltage amplitude of the in-phase component of the voltage command to the first inverter within a range of 0≦V_(AI)≦V_(M) to achieve a desired reference output power Po,ref, wherein V_(M) corresponds to a maximum peak ac voltage rating of the first inverter.
 12. The method of claim 10 wherein setting a quadrature-phase component of a voltage command to the second inverter comprises: setting an amplitude of a quadrature-phase component of a voltage command to the second inverter to be within the range of 0≦V_(BQ)≦V_(M) wherein V_(M) corresponds to a maximum peak ac voltage rating of the first inverter.
 13. The method of claim 12 wherein: setting a quadrature-phase component of a voltage command to the second inverter comprises setting the amplitude of a quadrature-phase component of a voltage command to the second inverter to drive capacitive components of the first inverter loading to zero, and wherein in response to the load being inductive, the quadrature-phase component of a voltage command to the second inverter becomes zero.
 14. The method of claim 10 wherein setting the amplitude of the in-phase component of a voltage command to the second inverter comprises: setting the amplitude of the in-phase component of the voltage command to the second inverter within the range of 0 to (V_(M) ²−V_(BQ) ²)^(1/2).
 15. The method of claim 10 wherein the in-phase component of a voltage command to the second inverter is selected to drive an in-phase current I_(AI) of the first inverter towards zero.
 16. The method of claim 15 wherein selecting the in-phase component of a voltage command to the second inverter is limited by: (1) the requirement that the amplitude of the quadrature-phase component of a voltage command to the second inverter be within the range of 0≦V_(BQ)≦V_(M); and (2) the allowed total operating voltage of the second inverter.
 17. The method of claim 10 wherein the first reference value is zero.
 18. A method for providing efficient delivery of high frequency (HF) power into a load having a variable load impedance, the method comprising: (a) controlling a first inverter to achieve a desired radio frequency (RF) power level at an RF output thereof; and (b) controlling a second inverter such that the second inverter drives substantially any capacitive component of the first inverter loading to substantially zero, and a quadrature-phase component of a voltage command provided to the second inverter becomes zero when the load is inductive such that the second inverter delivers a real component of the output power having an amplitude within its voltage rating while concurrently maintaining an in-phase current sourced by the first inverter to be substantially zero or positive such that the first and second inverters have presented thereto a load impedance having a resistive/inductive characteristic.
 19. The method of claim 18 further controlling the first and second inverters to have an inductive loading component limited to that necessary for supplying any reactive component of a load current while at the same time realizing zero-voltage switching (ZVS) of both inverters.
 20. The method of claim 19, wherein in response to the load having an inductive impedance characteristic, the second inverter delivers as much of the real component of the HF output power as possible within its voltage rating while concurrently maintaining the in-phase component of current sourced by the first inverter to be zero or positive
 21. A method for providing efficient delivery of radio frequency (RF) power from an inverter into a load having a variable load impedance, the method comprising: (a) controlling a first inverter to achieve a desired RF power level at an RF output thereof; and (b) controlling a second inverter to drive capacitive components of first inverter loading to substantially zero.
 22. The method of claim 21, wherein in response to the load being inductive a, quadrature-phase component of a voltage command provided to the second inverter becomes zero such that the second inverter delivers as much of a real component of the output power as possible within its voltage rating while concurrently maintaining a real power sourced by the first inverter to be substantially zero or positive.
 23. The method of claim 21 further comprising controlling the first and second inverters such that each inverter always has presented thereto a load impedance having a resistive/inductive characteristic with the inductive loading component limited to that necessary for supplying any reactive component of a load current while at the same time realizing zero-voltage switching (ZVS) of both inverters.
 24. A power delivery system comprising: a controller; an immittance converter; and a pair of inverters coupled to each other, said immittance converter and said controller and responsive to control signals provided by said controller such that each inverter always has presented thereto a load impedance having a resistive/inductive characteristic with the inductive component of the resistive/inductive characteristic limited to that necessary for supplying any reactive component of a load current while at the same time realizing zero-voltage switching (ZVS) of both inverters. 